Portrait lens system formed with an adjustable meniscus lens

ABSTRACT

A portrait lens configuration for meeting handheld device form factor constraints. First and second meniscus lenses each have a reflective surface to provide internal reflections for transmitting light toward a focal plane. A third lens is positioned between the meniscus lenses and the focal plane. The first lens includes an anterior concave surface having a reflective material extending over a portion thereof. Light received by the first meniscus lens can be transmitted therethrough. The reflective material is positioned along the anterior concave surface to receive light transmitted therethrough and reflected back from the second lens. In an associated method the first meniscus lens is positioned to receive light through a first of two opposing refractive surfaces. After each lens provides an internal reflection, reflected light is transmitted through the second of the two opposing surfaces and then through a bore positioned within the second lens to the third lens.

CLAIM OF PRIORITY

This application claims priority to provisional patent application Ser.No. 62/467,647, titled Portrait Lens Concept in a Mobile Phone Camera,filed 6 Mar. 2017.

FIELD OF THE INVENTION

This invention relates to lens systems and, more specifically, tosystems and methods for portraiture photography. In one series ofembodiments the invention provides a portraiture lens system suitablefor mobile phone cameras.

BACKGROUND OF THE INVENTION

The convenience of an imaging device integrated within a handheldelectronic device has spurred advancement of technology to improvedigital image quality within small form factor constraints.Specifically, there have been significant advancements in imageresolution, moving lenses, autofocus features and dual lens systemsproviding optical zoom capabilities. Yet smart phone cameras have beenoptically limited due to the constraints of the compact format. To someextent the space constraints have been dealt with by folding the opticalpath to provide longer focal lengths and larger images. See, forexample, U.S. 2016/0231540 which discloses use of folded optics toprovide a telephoto lens system compatible with space constraints of asmart phone. There is continued demand for improved designs that enhancethe versatility of mobile phone cameras and also improve the imagequality of lens systems within the constraints of small form factorcameras.

SUMMARY OF THE INVENTION

According to one series of embodiments of the invention, a lensconfiguration is designed to acquire portrait images. The system isadaptable, e.g., scalable, for meeting the varied factor constraints toeffect integration in a handheld camera device, such as a mobile phoneor tablet computer. The configuration includes first and second meniscuslenses. Each meniscus lens has a reflective surface to provide internalreflections. The meniscus lenses are aligned along an optical axis fortransmitting light from an object along a path toward a focal plane. Atleast a third lens is positioned between the meniscus lenses and thefocal plane. The first lens includes an anterior concave surface havinga reflective material extending over a portion thereof so that lightreceived by the first meniscus lens from the object can be transmittedthrough the first lens. The reflective material is positioned along theanterior concave surface to receive light which has been transmittedthrough the first lens and reflected back from the second meniscus lens.Light received by the reflective material may be transmitted along apath which passes through the second meniscus lens and then through thethird lens. The path of reflected light transmitted through the secondmeniscus lens may pass through a bore situated in the second lens beforereaching the third lens. The path of the reflected light transmittedthrough the second meniscus lens may pass entirely through the borewhich may be centrally situated in the second lens. The third lens maybe a negatively powered lens or group of lenses serving to adjust focusof light or change image size along the focal plane.

In the lens configuration a posterior surface of the first meniscus lensand an anterior surface of the second meniscus lens are surfaces facingone another and having complementary radii of curvature enabling saidsurfaces to be brought within 0.06 mm of one another.

Also, the bore may be centrally positioned within the second meniscuslens and may extend through a posterior surface of the second lens. Theposterior surface of the second lens may include a reflective materialproviding the reflective surface of the second meniscus lens, providingthe internal reflections therein. The reflective material extendsradially outward with respect to the optical axis and away from thebore.

Adjustment to focus objects at varied object distances L_(OBJ) along thefocal plane may be effected by movement of the third lens along theoptical axis. With this arrangement the lenses may be configured tofocus images of objects on the focal plane over a range of objectdistances L_(OBJ) extending from 500 mm or less, e.g., from 500 mm orless to L_(OBJ)=∞.

In another embodiment, adjustment to focus objects at varied objectdistances L_(OBJ) along the focal plane is effected by movement of thesecond meniscus lens along the optical axis. The lenses may beconfigured to focus images of objects on the focal plane over a range ofobject distances L_(OBJ) extending from 500 mm or less to L_(OBJ)=∞.

According to another series of embodiments of the invention, a lenssystem comprises a first meniscus lens, a second meniscus lens and athird lens each positioned along a common optical axis to transmit lightreceived from an object to a focal plane. The first lens includes aconcave transmissive first surface and a convex parabolic second surfacehaving a first radius of curvature. The second lens includes a concaveparabolic first surface characterized by a second radius of curvature,complementary to the first radius of curvature of the second surface ofthe first lens. The second lens also includes a convex second surfacehaving a bore positioned along the optical axis. When positioned betweenthe object and the focal plane, to provide an image of the object alongthe focal plane: (i) the concave, transmissive first surface of thefirst lens faces the object to receive and refract light traveling fromthe object for entry into the lens system through the first lens forfocusing along the focal plane; (ii) the concave parabolic first surfaceof the second lens is positioned to face the convex parabolic secondsurface of the first lens in spaced apart relation from the convexparabolic second surface of the first lens at a separation distance notexceeding 0.06 mm for all operative portions of the surfaces throughwhich light passes before becoming focused along the image plane; (iii)light from the object which is transmitted through the concave parabolicsecond surface of the second lens is internally reflected along thesecond surface of the second lens; (iv) the light internally reflectedalong the second surface of the second lens is then internally reflectedalong the first surface of the first lens; and (v) the light internallyreflected a second time enters the bore and is transmitted through thethird lens to the focal plane. Any or all refracting and reflectingportions of all surfaces may be aspheric.

In one embodiment, adjustment to focus objects at varied objectdistances, L_(OBJ), along the focal plane is effected by movement of thethird lens along the optical axis. Accordingly, the lenses may beconfigured to focus images of objects on the focal plane over a range ofobject distances L_(OBJ) extending from 500 mm or less. The lenses mayprovide a range of focus of images of objects on the focal plane forobject distances L_(OBJ) extending from 500 mm or less to L_(OBJ)=∞.

In another embodiment, adjustment to focus objects at varied objectdistances, L_(OBJ), along the focal plane is effected by movement of thesecond lens along the optical axis. This may change the separationdistance between the first and second lenses. The lenses may beconfigured to focus images of objects on the focal plane over a range ofobject distances L_(OBJ) extending from 500 mm or less to L_(OBJ)=∞.

According to still another embodiment of the invention, a method isprovided for generating an image of an object by providing a lightexpansion and image objective stage with a set of lenses comprisingfirst and second meniscus lenses, each arranged along an optical axis toprovide an internal reflection of light received from the object. Thefirst of the meniscus lenses is positioned to receive the light into thestage through a first of two opposing refractive surfaces. After each ofthe two lenses provides an internal reflection, the reflected light istransmitted through the second of the two opposing surfaces of the firstlens and then through a bore positioned within the second meniscus lensto a negative third lens. In one embodiment, the light expanding andcondensing stage provides light expansion before the light undergoes aninternal reflection in the second lens, and at least one of the internalreflections condenses the light.

BRIEF DESCRIPTION OF THE FIGURES

The following drawings are provided to facilitate understanding of theinventive concepts described in the written description which follows,where:

FIG. 1 illustrates a configuration of a lens system according to a firstembodiment of the invention;

FIGS. 2A-2D are ray diagrams for the lens system of FIG. 1;

FIGS. 3A and 3B present on-axis and off-axis spot diagrams for the lenssystem of FIG. 1;

FIG. 4 illustrates a lateral color distribution for the lens system ofFIG. 1;

FIG. 5 illustrates a configuration of a lens system according to asecond embodiment of the invention;

FIGS. 6A-6D are ray diagrams for the lens system of FIG. 5;

FIGS. 7A and 7B present on-axis and off-axis spot diagrams for the lenssystem of FIG. 5;

FIG. 8 illustrates a lateral colour distribution for the lens system ofFIG. 5;

FIG. 9A presents, for the embodiment of FIG. 5, relative illuminationand distortion across a ten degree field, calculated for L_(OBJ)=500 mmand a wavelength of 0.587 μm;

FIG. 9B presents, for the embodiment of FIG. 5, field curvaturecalculated for L_(OBJ)=500 mm and a wavelength of 0.587 μm; and

FIG. 9C presents, for the embodiment of FIG. 5, distortion across a tendegree field calculated for L_(OBJ)=500 mm and a wavelength of 0.587 μm.

Like reference numbers are used throughout the figures to denote likecomponents. Numerous components are illustrated schematically, it beingunderstood that various details, connections and components of anapparent nature are not shown in order to emphasize features of theinvention. Various features shown in the figures are not to drawn scale.

DETAILED DESCRIPTION OF THE INVENTION

Conventionally, portraiture photography is performed with a relativelylong focal length lens providing a 28-30 degree field of view (FoV). Atypical focal length, f, for a 24×326 mm full frame camera is 85 mm. Byway of comparison, cameras in mobile phone devices typically provideimages over a 76-78 degree field, more than twice the normal FoV rangefor portraiture applications. The face in a portrait image iswell-focused to exhibit a desired level of detail while backgroundfeatures are deliberately blurred (e.g., optically defocused for distantobjects), in order to reduce unnecessary distraction from the mainsubject in the image.

The extent of the background blur is inversely proportional to the depthof field, ΔL, the distance in object space over which a given lensconfiguration provides an acceptable focus. For a given linear (lateral)magnification, m, from object space to image space, and a given objectdistance, L_(OBJ), measured from the object to the lens, the depth offocus, Δz, in image space may be expressed as Δz=2λf²/D² where D is thelens aperture diameter. Also, noting that m², the longitudinalmagnification, may be expressed as (f/L_(OBJ))², the depth of field, ΔL,may be expressed as ΔL=Δz/m², and the depth of field reduces toΔL=2λ(L _(OBJ) /D)².

With the depth of field, ΔL, inversely proportional to the square of thelens aperture diameter D, for a given object distance L_(OBJ), use of arelatively large diameter camera lens is advantageous. When D isincreased by a factor of two, the background blur increases by a factorof 4. Maintaining lens f-number f/D leads to a longer focal length. Inthe past, it has not been feasible to incorporate this level of opticalperformance in a mobile phone housing having a z-dimension on the orderof five mm. Embodiments of the invention comprise folded opticalsystems, or catadioptric lens systems, providing double ray paths. Thesefeatures can, alone or in combination, enable an extended focal lengthto retain a lens speed on the order of, for example, f/2, within thefive mm format.

Optical systems with a double ray path usually feature a centralobscuration, which can also be beneficial for the portrait lens concept.The central part in the background blur is formed at a slower f-numberand therefore exhibits a greater depth of focus, i.e., staying in focusover larger object-background distances. Point-like highlights in theimage background might noticeably appear as circles, missing theircentral portion due to the shadow of the central obscuration on theimage sensor. For more aesthetically pleasing, uniform bokeh, thecentral part of such circles may be filled with similar light levelbackground in digital post-processing. This requires extra imageprocessing for such lenses.

In high-resolution applications such as iris imaging for identityverification, or group photography, the central obscuration is notdesirable, since it noticeably reduces image contrast. Embodiments ofthe invention are based on recognition that, for portraiturephotography, diffraction-limited image quality need not be arequirement, and some residual aberrations are acceptable or evendesirable for achieving a so-called “soft” portrait effect. Each ofthese considerations render the disclosed optical design featuresadvantageous for portrait lens applications. For these reasons, thoseskilled in the art will recognize that numerous combinations of thedisclosed design features will result in suitable lens system designsfor portraiture photography.

FIGS. 1 and 5 illustrate two embodiments of a lens system 10 accordingto the invention. A first meniscus lens 12, a second meniscus lens 14and a negative-powered third lens 16 are arranged along a common opticalaxis, O. The system transmits light received from an object 18 to asensor array 20 positioned in a focal plane 22 along which an image ofthe object is presented. In the embodiment illustrated in FIGS. 1 and 2,the lens 16 serves as a field lens which is adjustable along the opticalaxis to effect image focusing over an object distance, L_(OBJ), rangingfrom 500 mm (FIGS. 2A and 2C) or less to L_(OBJ)=∞ (FIGS. 2B and 2D). Inthe embodiment illustrated in FIGS. 5 and 6, the second meniscus lens 14is adjustable along the optical axis to effect image focusing over theobject distance which, again, ranges from L_(OBJ)=500 mm or less toL_(OBJ)=∞. More generally, embodiments of the systems 10 and 100 mayprovide a range of focus for object distances of 500 mm or less toL_(OBJ)=∞.

Still referring to FIG. 1, an adjustable stop 24 is positioned in frontof the first meniscus lens 12, which lens receives light from the object18 into the system 10. In accord with the disclosed design, the stop isplaced at the periphery of the front surface 12 a of the lens 12. Itwill be recognized by those skilled in the art that, for the exemplarysystem specifications, small displacements of the stop position from theillustrated location will degrade image quality.

The lens 12 includes (i) a concave aspheric surface as the front lens 12a, which faces the object and (ii) a convex parabolic surface 12 b ofradius −6.32 mm facing the focal plane 22. The surface 12 a is partiallytransmissive and partially reflective, with a peripheral portion of thelens 12 positioned to refract light entering the lens assembly. For theillustrated embodiments, a central region along the surface 12 aincludes a reflective surface 12R, e.g., a silvered surface. The surface12R renders the central region of the surface 12 a opaque totransmission of light coming into the system and effects reflectionswithin the system. The surface 12R extends radially from the axis, O, adistance R₁=1.2 mm from the axis. A transmissive surface 12T extendsalong an outer portion of the lens surface 12 a, beginning at the radialdistance R₁=1.2 mm from the optical axis. The transmissive surface 12Textends to a radial distance R₂=2 mm from the optical axis, O, allowingrefraction of light entering into the system 10 for expansion.

A concave parabolic first optical surface 14 a of the second lens ofradius −6.32 mm faces the convex parabolic surface 12 b of the firstlens in a spaced-apart relation indicated by gap G, e.g., an air gap.The surface 14 a has a radius of curvature complementary to the radiusof curvature of the convex parabolic surface 12 b. For a given value ofgap G, the magnitude of the radius of curvature of each surface 12 b, 14a is substantially the same. Generally, for applications of the lenssystem 10, the separation distance between adjacent portions the lenses12 and 14 may extend to 0.06 mm or more. In the embodiment of FIG. 2,gap G provides a fixed spacing between the lenses 12 and 14 which, asmeasured along the optical axis, is a 0.01 mm separation betweenadjacent surfaces. By stating that the magnitude of the radius ofcurvature of each surface 12 b and 14 a is substantially the same, it ismeant that along operative portions of the optical surfaces, foradjacent portions of the surfaces, the difference in value between themagnitudes of the complementary radii of curvature is sufficiently smallthat the operative portions of the lens surfaces adjacent one another donot come into physical contact or otherwise exhibit misalignment whichcauses noticeable degradation in image quality.

A convex, aspheric second optical surface 14 b of the second lens facesthe focal plane 22. The surface 14 b is made reflective with a coating14R (e.g., a silvered surface) formed thereon to internally reflectlight transmitted through the lens surface 14 a. The second lens 14includes a bore 26 which extends through each of the lens surfaces 14 a,14 b. The bore shape is defined by a lens bore surface 14 _(BS) whichextends along an interior central portion of the lens body. The bore 26is symmetrically aligned about the optical axis such that, at each pointalong the optical axis within the bore, the surface 14 _(BS) resides afixed radial distance R_(B) from the optical axis, while the radialdistance R_(B) varies as a function of position along the optical axis.In the disclosed embodiments the bore shape defined by the surface 14_(BS) is frusto-conical. The size of the bore R_(B) increases from aminimum radial dimension near the surface 14 a.

Along the refractive surface 14 a, R_(B)=1.17 mm. The lens surface 14 aextends radially outward from R_(B)=1.17 mm to the lens periphery, e.g.,to a radial distance of 2.5 mm from the optical axis. Commensurate withthe coating 14R, the reflective lens surface 14 b extends radiallyoutward from points where the surface 14 _(BS) and the surface 14 bmeet. This corresponds to a radial distance R_(B) of 3.0 mm, measuredfrom the optical axis to the lens surface 14 b. The reflective lenssurface 14 b may fully extend to the lens periphery, a radial distanceof 3.0 mm from the optical axis. In the illustrated embodiments the bore26 is an air cavity into which converging light internally reflectedwithin the first lens 12 is transmitted directly to the third lenswithout propagating through the body of the second lens 14. In theembodiment of FIGS. 1 and 2 the third lens 16 is movable along the boreto focus through the entire range of object distances L_(OBJ). The lens16 comprises an anterior first surface 16 a and a posterior surface 16 bwhich is convex in the paraxial region and concave in the marginalregion.

Having an adjustable position along the optical axis, the lens 16 actsas both a field lens and a refocusing element. For this configuration,FIGS. 2A-2D illustrate select ray paths of incoming light travellingfrom the object 12 and into the lens system 10.

FIGS. 2A and 2B illustrate the paths of rays coming into the system 10when the object 18 is positioned on-axis. In FIG. 2A the lens 16 ispositioned to focus the object on the sensor array 20 at a distanceL_(OBJ)=500 mm. In FIG. 2B the lens 16 is positioned to focus the objecton the sensor array 20 when L_(OBJ)=∞. FIGS. 2C and 2D illustrate thepaths of rays from the object 18 when the object is positioned eightdegrees off-axis. In FIG. 2C the lens 16 is positioned to focus theobject on the sensor array 20 at the distance L_(OBJ)=500 mm. In FIG. 2Dthe lens 16 is positioned to focus the object on the sensor array 20when L_(OBJ)=∞.

Light travelling from object 12 enters the system 10 through theanterior transmissive lens surface 12T of the first lens 12, passesthrough the opposing posterior second optical surface 12 b, through gapG and through anterior surface 14 a of the second lens. The transmittedlight then undergoes first internal reflections IR1 along the posteriorconvex aspheric surface 14 b, returning through the lens surface 14 a ofthe second lens 14, through gap G and through the posterior second lenssurface 12 b of the first lens 12 to be incident along the reflectivesurface 12R where the light undergoes second internal reflections IR2.After undergoing the multiple internal reflections within the lenses 12and 14, a portion of the light exits the first lens 12 through theposterior second lens surface 12 b for entry into the bore 26 fortransmission through the third lens 16 to the focal plane 22. With thelenses 12 and 14 providing an objective stage, the adjustable lens 16serves to adjust image quality, sharpness, depth or size and refocus theimage for varied object distances. In other embodiments, the lens 16could be a field lens stage comprising multiple lens elements to, forexample, correct challenging off-axis aberrations including but notlimited to field curvature and chief ray angle.

For an exemplary application, the complementary radii of curvature forthe parabolic lens surfaces 12 b and 14 a are −6.32 mm. The sag, z, foreach rotationally aspheric lens surface 12 a, 14 b, 16 a and 16 b havinga vertex radius of curvature, r₀, is calculable from the followingexemplary sag equation:z=y ²/2r ₀ +Ay ⁴ +By ⁶ +Cy ⁸ +Dy ¹⁰ +Ey ¹²where y is the radial coordinate perpendicular to the optical axis. Thesag equation comprises (i) a second order term y²/2r₀, descriptive of aparabolic base term, the more general form of which includes a conicconstant term describing conical departure from the familiar sphere, and(ii) a series of higher order even asphere polynomial terms (e.g., tothe 12^(th) order) where the polynomial coefficients are given in Table1A. For further discussion, see Fisher, et al., Optical System Design,Second Edition., McGraw Hill, SPIE Press 2008. See, also, O'Shea,Elements of Modern Optical Design, John Wiley & Sons, Inc. 1985.

For the embodiment of FIGS. 1, 2A and 2C, with L_(OBJ)=500 mm, the backfocal distance is 0.59 mm and the axial distance between the posteriorsurface 12 b of lens 12 and the anterior surface 16 a of lens 16 is 1.66mm. Tables 1A and 1B provide exemplary specifications for lenses 12, 14and 16 according to the embodiment of FIGS. 1 and 2.

TABLE 1A Sag Equation Polynomial Coefficients for Lens System 10 Lens AB C D E 12 (anterior) −1.684 × 10⁻³   1.794 × 10⁻⁴ −9.421 × 10⁻⁵   2.086 × 10⁻⁵ −1.754 × 10⁻⁶ 14 (posterior) −2.646 × 10⁻⁴ −3.239 × 10⁻⁶  7.062 × 10⁻⁷  −7.953 × 10⁻⁸   3.033 × 10⁻⁹ 16 (anterior) 0.075000−0.030356 0.006816 −4.9181 × 10⁻⁴ 0 16 (posterior) 0.078579 −0.0258470.004187   1.2530 × 10⁻⁴ 0

TABLE 1B Lens Specifications for Embodiment of Lens System 10 LensAnterior Radius Posterior Radius Central Thickness Material Asphericity12 −7.581 mm  −6.323 mm 2.0 mm SF5 Anterior Surface 14 −6.323 mm −10.415mm 2.0 mm BK7 Posterior Surface 16 −3.325 mm  −6.790 mm 0.25 mm  BK7Anterior and Posterior Surfaces

To summarize features of the lens system 10, two meniscus lenses 12 and14 are brought together with their parabolic surfaces (each havingradius of curvature of −6.32 mm) in almost full contact (i.e., an axialseparation on the order of 0.01 mm). The other surfaces of these lensesare used to perform internal reflections, each being modified accordingto a 12^(th) order even asphere sag equation. With a portion of theaspheric surface 12A of the front lens used as a refractive surfacehaving an aperture diameter ranging from D_(min)=2.4 mm to D_(max)=4 mm,this results in transmission of approximately 64 percent of lightincident on the surface 12 a passing through the transmissive lenssurface 12T.

The second lens 14 includes a central bore opening which may, forexample, be cylindrical or frusto-conical in shape, through which lightpasses to the third lens 16, which acts as both a field lens andrefocusing element. The object distance range of focus is from infinityto 500 mm. The full field of view is 20 degrees, which corresponds to200 mm linear size in object space (at L_(OBJ)=567 mm) and 2.8 mm imagediameter on the sensor array 20, nominally sufficient to capture thehead of a subject at a minimum distance of about 600 mm.

The Total Track Length (TTL) based on the central thickness of thelenses is 4.5 mm. The image quality is diffraction limited (see FIG. 3)with an Airy disk radius, R_(Airy), of 1.4 microns, (i.e., R_(Airy)=1.22λf/D) which cannot be resolved by the smallest (0.9 micron) availablepixels. Thus, the lens is detector limited. Image distortion is aboutone percent at L_(OBJ)=500 mm and two percent for L_(OBJ) at infinity.The inner side of the lens 14, i.e., along the surface 14 _(BS),provides for baffling of stray light. Nonetheless, stray light bafflingcreates a significant vignetting effect for field angles larger than 6degrees. Spot diagrams for the lens system 10 are presented in FIG. 3 atL_(OBJ)=500 mm for points on-axis (FIG. 3A, left) and at the full fieldof 10 degrees (FIG. 3B, right). The legend in FIG. 3 refers towavelengths in μm. The data were acquired at 0.486133 μm, 0.587562 μmand 0.656273 μm. The Airy disk is shown as a circle with radius 1.38 μm.Lateral colour distribution, such as shown in FIG. 4, can be digitallycorrected.

FIGS. 5 and 6 illustrate a lens system 100 according to a secondembodiment of the invention where illustrated features are annotatedwith the same reference numerals assigned to like features of the firstembodiment as shown in FIGS. 1 and 2. A first meniscus lens 12, amovable second meniscus lens 14 and a fixed negative-powered third lens16 are arranged along a common optical axis, O. The lenses and othersystem components of FIGS. 5 and 6, while similar to the components ofthe first embodiment, have different specifications and relationships asnow described. The system 100 transmits light received from the object18 to a sensor array 20 positioned in a focal plane 22 along which animage of the object is presented. In the embodiment illustrated in FIGS.5 and 6, the second meniscus lens 14 is adjustable along the opticalaxis to effect image focusing over the object distance which, again,ranges from L_(OBJ)=500 mm (FIGS. 6A, 6C) or less to L_(OBJ)=∞ (FIGS.6B, 6D). Lens specifications for the embodiment of FIGS. 5 and 6 differfrom the lens specifications for the embodiment of FIGS. 1 and 2.

Still referring to FIG. 5, an adjustable stop 24 is positioned in frontof the first meniscus lens 12, which lens receives light from the object18 into the system 10. As noted for the embodiment of FIGS. 1 and 2, thestop is positioned at the periphery of the front surface 12 a of thelens 12. Small displacements of the stop position require modifying thesystem design to avoid degrading image quality.

The lens 12 includes (i) a concave aspheric surface as the front lens 12a, which faces the object and (ii) a convex parabolic surface 12 b ofradius −6.2 mm facing the focal plane 22. As described for the firstembodiment, the surface 12 a is partially transmissive and partiallyreflective, with a peripheral portion of the lens 12 positioned torefract light entering the lens assembly. For the illustratedembodiments, a central region along the surface 12 a includes areflective surface 12R, e.g., a silvered surface, which is a 12^(th)order even asphere. The surface 12R also renders the central region ofthe surface 12 a opaque to transmission of light coming into the systemand effects reflections within the system. The surface 12R extendsradially from the axis, O, a distance R₁=1.1 mm from the optical axis. Atransmissive surface 12T extends along an outer portion of the lenssurface 12 a, beginning at the radial distance R₁=1.1 mm from theoptical axis. The transmissive surface 12T extends to a radial distanceR₂=2 mm from the optical axis, O, allowing refraction of light enteringinto the system 100 for expansion.

A concave parabolic first optical surface 14 a of the second lens, ofradius −6.2 mm, faces the convex parabolic surface 12 b of the firstlens in a spaced-apart relation characterized by gap G, e.g., an airgap. The gap G provides a variable separation distance between lenses 12and 14 along the direction of the optical axis to effect focusing theimage along the focal plane 22 coincident with the sensor array 20 forvariable distances L_(OBJ). The surface 14 a has a radius of curvaturecomplementary to the radius of curvature of the convex parabolic surface12 b. The magnitude of the radius of curvature of each surface 12 b, 14a is substantially the same. The range of variable separation distancebetween adjacent portions the lenses 12 and 14, as measured along theoptical axis, extends from 0.002 mm to 0.04 mm. Generally, for otherembodiments of the lens system 100, the range of variable separationdistance between adjacent portions the lenses 12 and 14 may differ fromthe range suggested for embodiments according to FIGS. 5 and 6. Forexample, the range may extend to 0.06 mm or more. By stating that themagnitude of the radius of curvature of each surface 12 b and 14 a issubstantially the same, the meaning of ‘substantially’ is as describedwith respect to the embodiment of FIGS. 1 and 2 such that the differencein value between the magnitudes of the complementary radii of curvatureis sufficiently small that over the range of separation distance betweenadjacent portions the lenses 12 and 14, measured along the optical axis,operative portions of the two lens surfaces adjacent one another do notcome into physical contact or otherwise exhibit misalignment whichcauses noticeable degradation in image quality.

A convex, aspheric second optical surface 14b of the second lens facesthe focal plane 22. The surface 14 b is reflective, having a coating 14R(e.g., a silvered surface) formed thereon to internally reflect lighttransmitted through the lens surface 14 a. The reflective surface 14 bis also a 12^(th) order even asphere. The second lens 14 includes a bore26 which extends through each of the lens surfaces 14 a, 14 b. The boreshape is defined by a lens bore surface 14 _(BS) which extends along aninterior central portion of the lens body. As described for theembodiment of FIGS. 1 and 2, the bore 26 is symmetrically aligned aboutthe optical axis. At each point along the optical axis within the bore,the surface 14 _(BS) resides a fixed radial distance R_(B) from theoptical axis, while the radial distance R_(B) varies as a function ofposition along the optical axis. In the disclosed embodiments the boreshape defined by the surface 14 _(BS) is frusto-conical. The size of thebore R_(B) decreases from a maximum radial dimension near the surface 14a.

Commensurate with the coating 14R, the reflective lens surface 14 bextends radially outward from points where the surface 14 _(BS) and thesurface 14 b meet. This corresponds to a radial distance R_(B) of 3.0mm, measured from the optical axis to the lens surface 14 b. Thereflective lens surface 14 b may fully extend to the lens periphery, aradial distance of 3.0 mm from the optical axis.

Along the refractive surface 14 a, R_(B)=1.28 mm to allow light to passto the plano-concave field lens 16, with both optical surfaces of thelens 16 being 10^(th) order even aspheres. The lens surface 14 a extendsradially outward from R_(B)=1.28 mm to the lens periphery, e.g., to aradial distance of 2.66 mm from the optical axis. Commensurate with thecoating 14R, the reflective lens surface 14 b extends radially outwardfrom points where the surface 14 _(BS) and the surface 14 b meet. Thiscorresponds to a radial distance R_(B) of 1.25 mm, measured from theoptical axis to the lens surface 14 b. The reflective lens surface 14 bmay fully extend to the lens periphery, e.g., a radial distance of 3.0mm from the optical axis. In the illustrated embodiments the bore 26 isan air cavity into which converging light internally reflected withinthe first lens 12 is transmitted directly to the third lens withoutpropagating through the body of the second lens 14. In the embodiment ofFIGS. 5 and 6, the second lens 14 is movable along the optical axis tofocus through a range of object distances L_(OBJ) from 500 mm to ∞. Theanterior first surface 16 a of the third lens 16 is aspheric andsubstantially flat, having an infinite radius of curvature. Theposterior surface 16 b is a concave aspheric surface.

For the configuration of FIG. 5, FIGS. 6A-6D illustrate select ray pathsof incoming light travelling from the object 12 and into the lens system10. FIGS. 6A and 6B illustrate the paths of rays coming into the system10 when the object 18 is positioned on-axis. In FIG. 6A the lens 14 ispositioned 0.04 mm away from the lens 12, as measured along the opticalaxis, providing a relatively large gap, G, between lenses 12 and 14, tofocus the object on the sensor array 20 at a distance L_(OBJ)=500 mm. InFIG. 6B the lens 14 is positioned 0.002 mm away from the lens 12, asmeasured along the optical axis, providing a relatively small gap, G,between lenses 12 and 14, to focus the object on the sensor array 20when L_(OBJ)=∞. FIGS. 6C and 6D illustrate the paths of rays from theobject 18 when the object is positioned ten degrees off-axis. In FIG. 6Cthe lens 14 is positioned 0.04 mm away from the lens 12, as measuredalong the optical axis, providing a relatively large gap, G, betweenlenses 12 and 14, to focus the object 12 on the sensor array 20 at thedistance L_(OBJ)=500 mm. In FIG. 6D the lens 14 is positioned 0.003 mmaway from the lens 12, as measured along the optical axis, providing arelatively small gap, G, between lenses 12 and 14, to focus the objecton the sensor array 20 when L_(OBJ)=∞.

Referring to FIGS. 6A-6D, light travelling from object 18 enters thesystem 100 through the anterior transmissive lens surface 12T of thefirst lens 12, passes through the opposing posterior second opticalsurface 12 b, through gap G and through anterior surface 14 a of thesecond lens. The transmitted light then undergoes first internalreflections IR1 along the posterior convex aspheric surface 14 b,returning through the lens surface 14 a of the second lens 14, throughgap G and through the posterior second lens surface 12 b of the firstlens 12 to be incident along the reflective surface 12R where the lightundergoes second internal reflections IR2. After undergoing the multipleinternal reflections within the lenses 12 and 14, a portion of the lightexits the first lens 12 through the posterior second lens surface 12 bto pass through the bore 26 for transmission through the third lens 16to the focal plane 22. With the lens 12 serving as an objective, theadjustable lens 14 serves to adjust image quality, sharpness, depth orsize and refocus the image for varied object distances. The fixed lens16 could be a field lens stage comprising multiple lens elements to, forexample, correct challenging off-axis aberrations including but notlimited to field curvature and chief ray angle.

For an exemplary application of the lens system 100, the complementaryradii of curvature for the parabolic lens surfaces 12 b and 14 a areeach −6.2 mm. The sag, z, for each rotationally-symmetric aspheric lenssurface 12 a, 14 b, 16 a and 16 b having a vertex radius of curvature,r₀, is calculable from the foregoing exemplary sag equation.

For the embodiment of FIGS. 5 and 6, with L_(OBJ)=500 mm, the back focaldistance is 0.35 mm and the axial distance between the posterior surface12 b of lens 12 and the anterior surface 16 a of lens 16 is 1.0 mm.Tables 1A and 1B provide exemplary specifications for lenses 12, 14 and16 for an embodiment of the system 100.

TABLE 2A Sag Equation Polynomial Coefficients for Lens System 100 Lens AB C D E 12 (anterior) −9.859 × 10⁻⁴ −1.085 × 10⁻⁴   4.2012 × 10⁻⁵ −9.256 × 10⁻⁶   7.5128 × 10⁻⁷ 14 (posterior) −3.172 × 10⁻⁴   3.938 ×10⁻⁵  −8.186 × 10⁻⁶   7.6567 × 10⁻⁷  −2.639 × 10⁻⁸ 16 (anterior)0.0717862 −0.125670 0.08240864 −0.01829125 0 16 (posterior) 0.136990−0.1715486 0.0772950  −6.929 × 10⁻³ 0

TABLE 2B Lens Specifications for Example Embodiment of Lens System 100Lens Anterior Radius Posterior Radius Central Thickness MaterialAsphericity 12 −6.9 mm  −6.2 mm  3.0 mm SF5 Anterior Surface 14 −6.2 mm−10.0 mm  1.0 mm BK7 Posterior Surface 16 infinity    7.8 mm 0.25 mm BK7Anterior and Posterior Surfaces

To summarize features of the system 100, two meniscus lenses 12 and 14are brought close together with their parabolic surfaces (each havingradius of curvature of −6.32 mm) in almost full contact (i.e., an axialseparation on the order of 0.01 mm). The other surfaces of these lensesare used to perform internal reflections, each being modified accordingto a 12^(th) order even asphere sag equation. With a portion of theaspheric surface 12A of the front lens used as a refractive surface,having an aperture diameter ranging from D_(min)=2.2 mm to D_(max)=4 mm,this results in transmission of approximately 70 percent of lightincident on the surface 12 a passing through the transmissive lenssurface 12T. The second lens 14 includes a central bore opening whichmay, for example, be cylindrical or frusto-conical in shape, throughwhich light passes to the third lens 16, which acts as both a field lenswhile the second lens 14 acts as a refocusing element. The objectdistance range of focus is from infinity to 500 mm. The full field ofview is 20 degrees, which corresponds to 200 mm linear size in objectspace (at L_(OBJ)=567 mm) and a 2.8 mm image diameter on the sensorarray 20, nominally sufficient to capture the head of a subject at aminimum distance of about 600 mm.

The Total Track Length (TTL) based on the central thickness of thelenses is 4.6 mm. Operating at about f/1.8 the image quality of the lenssystem 100 is diffraction limited over twenty degrees full field (seeFIG. 7) with an Airy disk radius, R_(Airy), of 1.28 microns, whichcannot be resolved by using 2 pixels, since the current smallest pixelavailable is 0.9 micron. Thus, the lens is detector limited. Imagedistortion is less than 0.3 percent from L_(OBJ) from 500 mm toinfinity. The inner side of the lens 14, i.e., along the surface 14_(BS), provides for baffling of stray light. Field angles larger thaneight to nine degrees are partly vignetted by lens 14. Spot diagrams forthe lens system 100 are presented in FIG. 7 at L_(OBJ)=500 mm for pointson-axis (FIG. 3A, left) and at the full field of 10 degrees (FIG. 3B,right). The legend in FIG. 7 refers to wavelengths in μm. The data wereacquired at 0.486133 μm, 0.587562 μm and 0.656273 μm. The Airy disk isshown as a circle with radius 1.28 μm.

Lateral colour distribution for the system 100, such as shown in FIG. 8,can be digitally corrected. Image distortion in the system 100 is wellcontrolled. The maximum value does not exceed ±0.3%. The distortioncurve does not change when refocusing from the object distanceL_(OBJ)=500 mm to L_(OBJ)=∞. This feature is advantageous in view ofimage processing required for lateral colour correction. For the lenssystem 100, FIGS. 9A to 9C respectively present relative illumination,field curvature and distortion across a ten degree field, calculated forL_(OBJ)=500 mm and a wavelength of 0.587 μm.

Embodiments of a small form-factor lens system have been described whichis suitably sized for use within the form factor of a smartphone casing.Embodiments of the invention provide an alternative to the multi-elementlens systems which are limited in terms of available degrees of freedomand ability to meet desirable metrics such as low f-number and largeaperture. For applications specifically directed to portraiturephotography with a dual lens system camera in a mobile phone device, thedesign is not constrained to the conventional requirement for anall-round high-performing lens, which normally precludes attainingcertain performance specifications at the expense of compromisinganother specification.

To achieve a desired reduction in depth of field (DoF), embodiments arebased on the geometrical relationship between DoF and lens aperturediameter, combining a relatively large diameter that reduces depth offield (e.g., by a factor of four) with f/D yielding a relatively large

focal length. Exemplary systems are based on a catadioptric lens designwith a double ray path, this reducing the field of view. Unlike typicallens designs used in mobile phone devices, larger diameter lenses areincorporated to reduce the depth of field by a factor of four or larger.Specifically, the disclosed lens systems each exhibit a depth of fieldat 500 mm reduced by a factor of four compared to typical lenses withD=2 mm. For the system 10, with L_(OBJ)=∞, the central thickness is 4.5mm, whereas f=7.9 mm, having a tele-photo effect of 1.76. WithL_(OBJ)=∞, the central thickness of the system 100 is 4.6 mm and f=7.2mm, giving this design a tele-photo effect of 1.57. The fast f/2.0 lenswith central obscuration of 2.4/4=0.60 helps reduce depth of field withthe system 10. The fast f/1.8 lens with central obscuration of2.2/4=0.55 helps reduce depth of field with the system 100. The systems10 and 100 exhibit diffraction-limited image quality for R, G and Bwith: for the system 10, an Airy disk radius of 1.4 μm (pixel limited)and, for the system 100, an Airy disk radius of 1.3 μm (pixel limited).With the bore 26 of the system 10 extending 2 mm along the optical axis,the bore surface 14 _(BS) advantageously acts to provide relativelyeffective stray light baffling. The system 100 exhibits good relativeillumination with only small vignetting at the edge of the field, andfocusing over the entire range is effected with movement of lens 14 byonly 0.04 mm of travel. In the system 10, lens movement for focusingover the distance ranging from infinity to 500 mm is 0.57 mm.

The invention is not limited to the described embodiments, which may beamended or modified without departing from the scope of the presentinvention. Rather, the invention is only limited by the claims whichfollow.

The claimed invention is:
 1. A lens system comprising: first and second lenses aligned along an optical axis for transmitting light from an object along a path toward a focal plane, the first lens including an anterior first surface through which received light can enter into the lens system and a posterior convex parabolic second surface having a first radius of curvature, the second lens including an anterior concave parabolic first surface characterized by a second radius of curvature, complementary to the first radius of curvature of the second surface of the first lens, where the concave parabolic first surface of the second lens is positioned to face the convex parabolic second surface of the first lens in spaced apart relation from the convex parabolic second surface of the first lens.
 2. The lens system of claim 1 where the magnitude of the radius of curvature of the posterior convex parabolic second surface of the first lens and the anterior concave parabolic first surface of the second lens are substantially the same.
 3. The lens system of claim 2 where, along operative portions of the optical surfaces, for adjacent portions of said surfaces, the difference in value between the magnitudes of the complementary radii of curvature is sufficiently small that the operative portions of said lens surfaces adjacent one another do not come into physical contact or otherwise exhibit misalignment which causes noticeable degradation in image quality.
 4. The lens system of claim 1 where the concave parabolic first surface of the second lens is spaced apart from the convex parabolic second surface of the first lens by a fixed gap distance measured along the optical axis.
 5. The lens system of claim 1 where the fixed gap distance measured along the optical axis does not exceed 0.06 mm for all operative portions of the spaced apart surfaces through which light passes before becoming focused.
 6. The lens system of claim 4 further including a third lens adjustably positionable along the optical axis between the second lens and the focal plane for focus adjustment of the image as a function of change in object distance L_(OBJ) from the posterior surface of the first lens.
 7. The lens system of claim 1 where the concave parabolic first surface of the second lens is spaced apart from the convex parabolic second surface of the first lens by a gap distance measured along the optical axis, and the gap distance is adjustable along the optical axis for focus adjustment of the image over a range in object distance L_(OBJ) measured from the posterior surface of the first lens.
 8. The lens system of claim 7 where the adjustable gap distance, as measured along the optical axis, does not exceed 0.06 mm for all operative portions of the spaced apart surfaces through which light passes before becoming focused.
 9. The lens system of claim 1 where the anterior first surface of the first lens includes a concave parabolic surface positioned to receive and refract light traveling from an object for entry into the lens system-through the first lens for focusing along the focal plane.
 10. The lens system of claim 1 where the first lens is a meniscus lens.
 11. The lens system of claim 1 where the second lens is a meniscus lens.
 12. The lens configuration of claim 1 where the lenses are configured to focus images of objects on the focal plane over a range of object distances L_(OBJ) extending from 500 mm or less to L_(OBJ)=∞.
 13. The lens configuration of claim 1 where the second lens includes a bore positioned along the optical axis.
 14. The lens configuration of claim 13 where the path of light transmitted through the first meniscus lens passes through the bore.
 15. The lens configuration of claim 13 where the path of light transmitted through the first meniscus lens passes through the bore.
 16. The lens configuration of claim 13 where the bore is centrally positioned within the second meniscus lens and extends through a posterior surface of the second lens and through a field lens.
 17. The lens configuration of claim 16 where the posterior surface of the second lens comprises a coating for internal reflection of light received from the object, causing light to pass through the first lens at least two times.
 18. A method for generating an image with light received from an object on an imaging sensor array plane, comprising: providing a first lens along an optical axis between the object and the sensor array, the first lens including an anterior first surface through which received light can enter into the lens and a posterior convex parabolic second surface having a first radius of curvature, providing a second lens along the optical axis, the second lens including an anterior concave parabolic first surface characterized by a second radius of curvature, complementary to the first radius of curvature of the second surface of the first lens, positioning the concave parabolic first surface of the second lens to face the convex parabolic second surface of the first lens in spaced apart relation from the convex parabolic second surface of the first lens.
 19. The method of claim 18 where the concave parabolic first surface of the second lens is spaced apart from the convex parabolic second surface of the first lens by a variable gap distance measured along the optical axis, the method further including adjusting the gap distance along the optical axis to adjust focus over a range in object distance L_(OBJ) measured from the posterior surface of the first lens. 